Many intelligent transportation systems are multi-agent systems, i.e., both the traffic participants and the subsystems within the transportation infrastructure can be modeled as interacting agents. The use of AI-based methods to achieve coordination among the different agents systems can provide greater safety over transportation systems containing only human-operated vehicles, and also improve the system efficiency in terms of traffic throughput, sensing range, and enabling collaborative tasks. However, increased autonomy makes the transportation infrastructure vulnerable to compromised vehicular agents or infrastructure. This paper proposes a new framework by embedding the trust authority into transportation infrastructure to systematically quantify the trustworthiness of agents using an epistemic logic known as subjective logic. In this paper, we make the following novel contributions: (i) We propose a framework for using the quantified trustworthiness of agents to enable trust-aware coordination and control. (ii) We demonstrate how to synthesize trust-aware controllers using an approach based on reinforcement learning. (iii) We comprehensively analyze an autonomous intersection management (AIM) case study and develop a trust-aware version called AIM-Trust that leads to lower accident rates in scenarios consisting of a mixture of trusted and untrusted agents.